determination of sampling constants for selenium in biological reference materials by neutron...

Fresenius J Anal Chem (1990) 338:399-407 Fresenius' Journal of

@ Springer-Verlag 1990

Determination of sampling constants for selenium in biological reference materials by neutron activation A. Chatt, R. R. Rao, C. K. Jayawickreme, and L. S. McDowell

Trace Analysis Research Centre, Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, B3H 4J1, Canada

Summary. A cyclic instrumental neutron activation analysis method has been used to calculate sampling constants and to evaluate homogeneity for Se in five biological reference and certified reference materials, namely NRC lobster hepatopancreas (RM TORT-l) , IAEA horse kidney (RM- H8), and NIST bovine liver (SRM-1577 a), oyster tissue (SRM-1566) and mixed diet (RM-8431). The between- weight-range heterogeneity has been observed to be no greater than the within-weight-range heterogeneity. The subsampling standard deviation (Ss) has been found to be less than the measurement standard deviation (Sin) for H-8 (> 5 mg sample) and TORT-1 ( > 50 mg). For 1577a, Ss is almost equal to Sin; while Ss is 2 - 3 times higher than S,~ for the other two materials. The sampling constants varied between 0.04 and 3.0 g for four materials while the mixed diet had a value of 31 g.

Introduction

Reference materials of certified trace element composition are used not only for evaluating the reliability of a new analytical method but also for ensuring the quality of data obtained in routine analysis programs. It is indeed a common practice to include an appropriate reference material in every batch of samples analyzed to test the accuracy of the laboratory results. These materials have also been used by a number of researchers as comparator standards for calculating elemental concentrations of their samples.

One of the most important properties of a reference material should be its high degree of homogeneity. Biological materials of natural origin, being inherently inhomogeneous, are certified for multi-element concentrations for sample sizes generally in the range of 100-250 mg. Sample-mass constraints are encountered in microanalytical techniques such as proton-induced X-ray emission, electrothermal atomization atomic absorption spectrometry, and in- ductively-coupled plasma atomic emission spectroscopy where solid samples are used directly. These modern analytical techniques are capable of analyzing very small sample masses, viz. sub-mg or mg, and require reference materials of similar size. In another situation, only a small amount of sample is available for analysis which must be done with a high degree of accuracy. In order to justify the usage of a certified reference material (CRM) or reference material

Offprint requests to. A. Chatt

(RM) at a mass lower than that recommended by the issuing agency, it is essential to evaluate their homogeneity at lower mass ranges and to determine the sampling constant for element(s) of interest.

The subject of sampling and quality assurance in chemical analysis has been reviewed by several authors [1 - 12]. The determination of sampling constants of selected elements in some geological [13-15] and biological [16- 20] reference materials have been reported in the literature. Homogeneity of a biological reference material is often evaluated by analyzing replicate samples of the same material for one or more of the major and minor elements. How- ever, homogeneity with respect to these elements does not guarantee the same for trace or ultratrace elements. Thus homogeneity of a reference material should-be ascertained for each trace element of interest. This paper presents results on the evaluation of homogeneity and calculation of sampling constants for Se in several biological CRMs and RMs by cyclic instrumental neutron activation analysis (CINAA).

Experimental

Reference materials

Five reference materials were selected for evaluating their homogeneity for Se. These were: lobster hepatopancreas (RM-TORT-I) supplied by the National Research Council of Canada (NRCC), horse kidney (RM-H-8) provided by the International Atomic Energy Agency (IAEA), and bovine liver (SRM-1577a), mixed diet (RM-8431) and oyster tissue (SRM-1566) purchased from the U.S. National In- situte of Standards and Technology (NIST). These materials were selected to cover a wide range of Se concentrations, viz. 0 . 2 - 7 ~tg/g. Separate portions (not used for analyzing Se content) of all reference materials were dried as recommended by the issuing agencies. Horse kidney and mixed diet samples were dried at 100°C for i h in an oven. Bovine liver, oyster tissue and lobster hepatopancreas were freeze- dried at a pressure of 0.5 mm Hg for 20 h.

Five mass ranges (namely 5 - 10, 45 - 55, 90-110 , 235 - 265, and 330-370 rag) were selected for preparing subsamples. Six replicates at each mass range were weighed into precleaned small 1.2 mL polyethylene vials. A trimmed polyethylene cap was inserted inside the vial and forced down to maintain an identical geometry of samples within the replicates at each mass range. The samples were then heat-sealed and packed into medium-size (7 mL) polyethylene irradiation vials for CINAA.

400

Selenium comparator standards

Selenium comparator standards were prepared by directly pipetting a known aliquot of ultrapure Se atomic absorption standard solution (SPEX Chemicals) by a calibrated Eppendorfpipet onto a sucrose matrix (Koch-Light Labora- tories) in 1.2 mL precleaned polyethylene vials. The comparator standards were of identical geometry and contained approximately similar amounts of Se as the reference materials. Six replicate comparator standards were prepared for each mass range and handled in exactly the same way as the reference materials.

Irradiations

Reference materials and comparator standards were irra- diated in the inner sites of the Dalhousie University SLOWPOKE-2 Reactor (DUSR) at a flux of either 5 x 10 * * or ] × 1012 n cm-2 s - i . Gamma-ray spectra were recorded using a 25 cm a Aptec hyperpure Ge Bullet detector with a full width at half-maximum (FWHM) of 2.1 keV and an efficiency of 8% measured at the 1332-keV photopeak of 6°Co. The detector was coupled to a Nuclear Data ND-66 model 4096-channel pulse height analyzer.

The Se content was measured using cyclic INAA with the automated transfer system via the 162-keV gamma-ray of 77mSe (half-life = 17.4 s). An irradiation time (tO of 2 0 - 60 s, decay time (te) of 5 s and counting time (re) of 20 - 60 s were employed. The number of cycles (n) were increased for each mass range until the counting statistics had improved to a desired value.

Theory of sampling constant

Techniques for sampling of materials with inhomogeneous distribution of the constituents of interest have been devel- oped for mineral evaluation [21- 28]. Wilson [29] observed that silicate rock powders from rocks with two or more mineral species would be heterogeneous and that the use of small samples for chemical analysis could give rise to large errors. To estimate the mass of an adequate sample for determining the element of interest in relation to the accuracy of the analytical method, Wilson calculated the subsampling error, S~. The magnitude of S~ was considered to depend on the mass of the sample, grain size distribution, density of particles, number of components, and the distribution of the analyte among the components. For an element distributed between the components A and B of a binary mixture, the subsampling error expressed as the relative standard deviation, S~ (%), can be written as:

S~(O/o ) = I00(CA -- C,) I fAf . dAd, 47cr3 }1/2

c ( d3 V/ 0)

where C, CA and Cu are the concentrations of the element in the entire sample and in its component phases A and B, respectively; d, da and du are the densities of the sample and its component phases A and B, respectively; r is the mean radius of particles, W is the weight of the sample, and fA and fB are the weight fractions of components A and B, respectively.

For a binary mixture with a trace element present in one minor phase A and absent in phase B, the above equation can be reduced to:

Ss(O/o)= looIdA4~r3ll/2 [ fA3 W J " (2)

In microanalytical methods, the sub-sampling error may be the largest contributor to overall error. In practice, Ss is minimized either by increasing the sample weight and/or by decreasing the particle size through grinding of the sample. Therefore, information about the particle size, density and composition of the sample are required for calculating subsampling error. In the absence of such information, In- gamells [27, 28] found that a well-mixed material could be characterized by the term sampling constant (K~) defined as:

ss (%) = [Ks~W] 1/~ (3)

where,

100 1 da 47rr3 1 K s = ~ f ~ - . (4)

Ks is a constant for the element under consideration in a given sample material of a particular particle size distribution. The sampling constant concept is not restricted only to sampling of geological materials but can be applied to biological samples as well as to any other fairly uniform material under investigation.

Calculation of sampling constant

Ingamells proposed a useful method for estimating the amount of subsample that should be used for chemical analysis such that the sampling uncertainty does not exceed a specified level and homogeneity can be ensured. The method involves the calculation of the sampling constant which is defined as the weight of the subsample necessary to ensure a relative subsampling error of 1% at the 68% confidence level in a single determination [28]. The sampling constant for an element of interest in a given sample is determined experimentally by replicate analysis of the sample of a given nominal weight using an analytical method of high precision and accuracy. The observed variability of the results then includes both analytical and subsampling variability. The subsampling error can be differentiated from the measurement error if there exists an independent estimate of the analytical error.

The overall variance (S 2) for a series of determinations includes the variance due to the measurement (S 2) and that due to the subsampling ($2):

so ~ = S~m + S~. (5)

In neutron activation analysis, measurement uncertainty (Sin) arises mainly due to the standard deviations of counting statistics (So), flux variations (Sf), sample geometry (Sg), blanks (Sb), comparator standards (Sos) and weighing errors (Sw):

s~ = s~ + s~ + s~ + s~ + sL + s~ . (6)

The flux variation in the inner irradiation site of the DUSR has been shown to be less than 1% [30]. If the counting geometry of the samples is made reproducible, and the weighing errors in preparing samples and the pipetting errors in preparing comparator standards are maintained at minimum, the contribution from Sf, Sg, Sw and Sos towards the analytical error can be considered negligible. Thus the major source of analytical uncertainty in NAA is most likely to

401

occur due to counting statistics, i.e. S2m ~-- S 2. Then the relative standard deviation due to subsampling error is given as :

& = (So ~ -- S~) ~/~ (7)

where So and S¢ are determined experimentally from a reasonable number of observations (n). The sampling constant is then calculated at a suitable weight range according to the equation:

Ks = S 2 (%) × W(in g) . (8)

Statistical considerations for evaluating uncertainty of data

Statistical calculations are used to help in the technical evaluation of the results. Let us consider that there are ' I ' independent data groups and each group has ' J ' observations. The variables Xaj ( i = 1,2 .... I a n d j = 1,2 .... J) are independent of one another where

E(Xij) = ]2i, Vat (Xu) = a 2 . (9)

I f all groups exhibit normal distributions with approximately the same variance a 2, then:

X i j = ]2i -~- ~ij ( 1 0 )

where each ~o is a random error term with mean zero and variance o -2.

)(i. is the sample mean of a random sample of size ' J ' and )7.. is the grand mean of all observations. The sample variance S 2 of the ith sample (whose value is computed from the observations in the ith row of the data group) is an unbiased estimator of a 2. There are ' J ' observations in each data group, the unweighted average of all S2's should give an unbiased estimator of cr 2. This estimator ^ 2 (erw) is called the within-weight-range-samples estimator of a 2 since it is obtained by pooling estimators from the individual samples.

I

s s~ ,=~ 1 { 1 1 J }

^2 : - - ~ - - ~ ( X i j - - J ~ i . ) e ( 1 1 ) a w = I I i=1 (J l) j = l

I J S s ( x u - 502

i = l j = l = (12)

i ( J - 1) Because each Xi. is the sample mean of a random sample of size ' J ' ,

Var 07~.) = [Vat (Xu)]/J = az/J (13)

and the variance of all these sample means of size ' I ' is given by:

I s ( £ . - Z . ) 2

i = 1 S 2 = (14)

( / - 1)

The Null hypothesis (Ho) and alternate (Ha) are given by:

Ho:]2* = ]22 . . . . . . ]21 = ]2 ( 1 5 )

Ha: at least two of ]2~'s are not equal. (16)

When Ho is true, all of the ]21's are equal then:

E()Ti.) = ]2 and var ()7i.) = az/ j (i = 1,2 .... /). (17)

Since S 2 is the variance of JTi.'s, S 2 is an unbiased estimator of the population variance, a2/J. Thus JS 2 is an unbiased estimator of a 2 when Ho is true. Because this estimator is based on sample means of ' I ' populations, it is often called the between-different-weight-range-samples estimator (82 ) of a 2.

I J ~ ( ~ ' ~ i . - ) ~ . . ) 2

i - 1 a2 = J S l = ( i s )

( i - 1)

I J z z (£i. - Y..)2

i = l j = l = (19)

( i - 1)

The decision as to whether or not Ho should be rejected will be made by comparing the two estimators of a 2. When an F-test reveals that the variation between the different- weight-range-sample sets is not significantly different from the variation within-weight-range-sample sets then all individual results, if normally distributed, can be used as estimates of the overal value.

F = ^2 ^2 (20) 0"B/0" w .

If the null hypothesis is true, 6 .2 and &2 should both estimate the same quantity and therefore F-ratio should be approximately 1 ; any variations away from I should occur only because of sampling errors.

The variance within-weight-range sample groups (3.2) is a good estimate of the overall population variance whether or not Ho is true. However, the variance between-weight- range sample groups (3-2) consists of the population variance plus an additional variance stemming from the differences between samples. Therefore, if the null hypothesis is false, 3.2 will be larger than 6-2w and the F-ratio will tend to be larger than 1. Larger F-values suggest that 3.2 has overesti- mated 02 and therefore the #i's are not equal. This indicates that the particular element of interest is inhomogeneously distributed in the sample material.

The value of the level of significance (~) gives the criterion for the rejection of/40 in favour of Ha if:

F~,a- 1), I u - 1) >- Tabulated F value. (21)

For the T or F distribution described by the null hypothesis, the 'p ' value is the smallest level of significance for which the observed sample statistics (T or F value) indicates rejection of Ho. To conclude the test, one has to compare the level of significance '~' with the 'p ' value. The acceptance or rejection of Ho is based on whether c~ < p or c~ > p, respectively. This criterion is true for an one-tail or two-tail test.

Results and discussion

Quantitation of Se by CINAA

The fast transfer cyclic system at the D U S R facility was designed and installed in collaboration with the Atomic En- ergy of Canada Limited - Commercial products. This system has been described in detail by Chatt and coworkers [31, 32]. The C I N A A method for the determination of Se, its precision and accuracy have previously been reported by the coauthors [33, 34]. The decision limit (Lc), the qualitative detection limit (LD) and the quantitative determination limit

402

(LQ) for measuring Se in different samples have been calculated according to the equations given by Currie [35]" 16

Lc (counts) = 2.33

LD (counts) = 2.71 + 4.65 ~ 14

LQ (counts) = 50 [1 + 1/(1 + #B/12.5)]

where #B is the number of counts in the background under the photopeak of interest. ,-, 12

The reproducibility of the cyclic transfer system at different cycles was evaluated by running six 100/~g Se standards using the following timing parameters: irradiation "~ 10 (tl) = 20 s, decay (ta) = 5 s, counting (to) = 20 s and transfer .~ (tt) = 5 s and number of cycles (n) = 10. The results showed an excellent reproducibility at each cycle with the fast cyclic ~ 8

Q transfer system at the DUSR facility. The precision measured in terms of relative standard deviation improved with the increase in the number of cycles. ~

Five biological reference materials were analyzed for Se "2 by the CINAA method. The precision and sensitivity of -~ the measurements were found to improve by increasing the m number of cycles. The degree of improvement was observed 4 to depend on the major elements present in the sample material, and to vary from material to material. In the absence of significant interference from the major elements, one could 2 expect the sensitivity to improve continuously with increasing number of cycles. However, in presence of large interferences from nuclides, produced from elements with high neutron absorption cross-sections, like short-lived 28A1 and 38C1 or long-lived 24Na, the number of times the material could be recycled is restricted thereby limiting the degree of improvement in sensitivity. An optimum improvement for the determination of Se in different reference materials at each mass level was achieved by selecting appropriate irradiation, decay and counting parameters coupled with the judicial choice of the number of cycles.

A typical example illustrating the optimization of 7 conditions for better sensitivity and precision for the determination of Se in IAEA horse kidney (H-8) at different mass levels is shown in Figs. 1 to 3. It clearly shows that the 6 LD and LQ were achieved in the first and seventh cycle, ,-., respectively, for 10 mg subsamples whereas the same were just achieved in the very first cycle for both 50 and 250 mg ~ s samples. It is evident from Fig. 3 that the measured Se con- = centration in the 250 mg subsamples decreased continuously with increasing number of cycles. This can be attributed to ~ the increasing dead-time and pulse pile-up losses (in counts) ~ due to continuously increasing background activities arising mainly from 24Na and 38C1. The results indicate that the Q o number of cycles required to achieve better counting ~ 3 statistics, good sensitivity and precision at 95% confidence "E = level lies in the range 10 -18 for 10 mg samples (Fig. 1), 5 - -~ 10 for 50 mg samples (Fig. 2) and a maximum of 2 cycles m 2 for 250 mg samples (Fig. 3).

Evaluation of sample homogeneity

A summary of analytical results obtained for samples at 4 or 5 different weight levels from the same bottle is shown in Tables i to 5. In each table, columns I to 3 represent the weight range of samples, Se content of individual samples and the mean value with the standard deviation (SD) for that weight-group set of samples, respectively. Student T-

\ .\

S0,%

3 2

-28

.24

.20

-16 ~o ~

. 1 2

I 0 0

0 4 8 12 18 20

Cycle number Fig. 1. The variation of counting statistics with cycle number for Se measurements in 10-rag horse kidney samples by CINAA

0

0

|

i

l 1

I\I , \ llliiii i l-r - -rTT

\,,

i

5

B~

4 8 oo

0

20 4 8 12 16

Cycle number Fig. 2. The variation of counting statistics with cycle number for Se measurements in 50-rag horse kidney samples by CINAA

v

O

ID

o

ID

~ 3

403

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

I t llIl 4.0 4.0

I

Ill I I i i i ~ i

3.2 I 3.2 I

i 2.4 \

".,,, N

1.6 "-. 1.6

"'-'---'---t ...... S O, %

0.8 ~ LQ 0,8

" ~ LD .... 0.0 0.0 , , ,

0 4 8 12 16 20

Cycle number

Fig. 3. The variation of counting statistics with cycle number for Se measurements in 250-mg horse kidney samples by CINAA

2.4 &

distr ibut ion tests on each set of da ta for different weight range samples at 95% confidence level against the pooled average or certified value was performed and the computed ' T ' and 'p ' values obtained are shown in the 4th and 5th columns of the tables of each reference material. These tables also list the overall relative s tandard deviat ion (So) for each set of results along with the measurement (counting) standard deviat ion (Sin --~ So).

The precision, with which the subsampling variabi l i ty can be estimated, mainly depends on the analytical error of the method. Cyclic I N A A being non-destructive with high sensitivity for Se determinat ion has an advantage since it is free from the possible errors that may arise from sample dissolution, contaminat ion, or loss during the sample prepa- rat ion step. The major source of r andom uncertainty that could develop in C I N A A is counting statistics. By choosing appropr ia te number of cycles, the uncertainty in the number of counts was brought under statistical control. The s tandard deviat ion of subsampling (Ss) of the reference materials was calculated by taking the square root of the value obtained from the difference between the overall variance (So 2) and the measurement variance (S2m) for each weight range of samples. The fraction of the overall uncertainty contr ibuted by subsampling 2 2 (S~/So) is also shown in the last column of the tables. The results indicate that this ratio varies with the weight range, the composi t ion and the nature of the reference material . The highest Ss values were observed in the lowest weight range of all reference materials.

Table 1. Standard deviation for Se measurement in NRC lobster hepatopancreas (RM-TORT-1) by CINAA

Weight range Se content Mean _+ SD Analysis of precision Overall Measmt Sub- Fraction (rag) (gg/g) (gg/g) (c~ = 0.05) SD (%) SD (%) sampling of uncer-

So Sm SD (%) tainty due T p Ss to sub-

sampling

5-- 10 5.36, 7.72, 7.02 6.62 __+ 0.94 0.10 0.93 14.3 7.4 12.2 0.73 5.59, 7.26, 6.79

45-- 55 6.76, 6.42, 6.57 6.57 + 0.37 0.63 0.56 5.6 4.8 2.88 0.26 7.02, 6.69, 5.93

90-- 110 6.82, 6.49, 6.75 6.70 + 0.29 0.29 0.78 4.3 3.5 2.50 0.34 7.12, 6.27, 6.72

235-265 6.35, 6.88, 6.68 6.76 ± 0.25 0.94 0.39 3.7 2.8 2.42 0.43 7.10, 6.76, 6.76

330--370 6.97, 6.50, 6.66 6.65 __+ 0.22 0.11 0.91 3.3 2.7 1.90 0.33 6.33, 6.70, 6.74

Table 2. Standard deviation for Se measurement in IAEA horse kidney (RM-H-8) by CINAA

Weight range Se content Mean +_ SD Analysis of precision Overall Measmt Sub- (mg) (gg/g) (gg/g) (c~ = 0.05) SD (%) SO (%) sampling

So S~ SD (%) T p Ss

Fraction of uncertainty due to subsampling

5 - 10 4.54, 4.64, 4.86 4.89 _+ 0.36 0.04 0.97 7.5 7.0 2.69 4.64, 5.17, 5.47

4 5 - 55 4.80, 4.83, 5.09 5.00 + 0.21 1.41 0.22 4.2 4.0 1.28 5.02, 5.36, 4.90

90-110 4.61, 4.82, 4.91 4.82 ± 0.18 0.82 0.45 3.8 3.2 2.05 5.13, 4.69, 4.75

235-265 5.09, 4.76, 4.71 4.90 ± 0.15 0.30 0.77 3.1 2.8 1.33 5.03, 4.89, 4.91

0.13

0.09

0.29

0.18

404

Table 3. Standard deviation for Se measurement in NBS oyster tissue (SRM-1566) by CINAA

Weight range Se content Mean + SD Analysis of precision Overall Measmt (mg) (I.tg/g) (gg/g) (c¢ = 0.05) SD (%) SD (%)

So Sm T p

Sub- sampling SD (%) &


5-- 10 2.28, 1.76, 1.90 2.30 4- 0.54 0.34 0.75 23.5 7.0 2.55, 2.04, 3.24

40-- 55 2.43, 2.26, 1.98 2.16 __+0.18 0.81 0.45 8.4 3.7 2.25, 2.03, 2.01

90--110 2.06, 2.36, 2.22 2.16 __+ 0.14 0.92 0.40 6.4 3.1 2.00, 2.10, 2.27

235-265 2.26, 2.34, 2.08 2.20 + 0.11 0.45 0.67 5.0 2.7 2.16, 2.08, 2.28

330--370 2.15, 2.26, 2.47 2.27 + 0.13 0.90 0.41 5.8 3.4 2.20, 2.38, 2.15

22.4

7.54

5.60

4.21

4.70

0.91

0.81

0.76

0.71

0.66

Table 4. Standard deviation for Se measurement in NBS mixed diet (RM-8431) by CINAA

Weight range Se content Mean ± SD Analysis of precision (mg) (ng/g) (ng/g) (c~ = 0.05)

T p

Overall Measmt Sub- SD (%) SD (%) sampling S o S m SD (%)

&


4 5 - 55 276, 367, 152 269 ± 76 0.31 0.77 28.2 11.5 25.8 219, 274, 324

90--110 186, 214, 236 250 __+ 51 0.45 0.67 20.4 8.5 18.6 269, 333, 260

235--265 292, 255, 238 265 ± 27 0.53 0.62 10.1 5.6 8.41 303,261,240

330--370 227, 233, 247 253 ± 23 0.68 0.53 9.1 3.8 8.27 252, 269, 288

0.83

0.83

0.69

0.83

Table 5. Standard deviation for Se measurement in NBS bovine liver (SRM-1577a) by CINAA

Weight range Se content Mean _+ SD Analysis of precision Overall Measmt Sub- (mg) (ng/g) (ng/g) (c~ = 0.05) SD (%) SD (%) sampling

S O S m SD (%) T p Ss


5 - 10 567, 698, 680 709 __+ 87 0.18 0'.87 12.3 7.5 9.75 0.63 773, 823,711

4 5 - 55 683, 732, 774 736 ± 52 0.99 0.37 7.1 4.8 5.23 0.54 668, 758, 802

90-110 768, 770, 703 724 ± 42 0.50 0.64 5.7 4.6 3.37 0.35 739, 673,688

235-265 625, 692, 645 682 ± 44 1.83 0.13 6.4 3.8 5.15 0.65 750, 699, 682

330-370 753, 731,735 724 ± 38 0.61 0.57 5.1 1.8 4.77 0.88 661,764, 702

The contr ibution of subsampling to overall uncertainty is 2 5 - 3 5 % in TORT-1 ( 4 5 - 3 7 0 mg), 1 0 - 3 0 % in horse kidney ( 5 - 2 6 5 mg), 4 0 - 6 0 % in bovine liver ( 5 - 2 6 5 mg), 7 0 - 8 0 % in oyster tissue ( 4 0 - 3 7 0 mg), and 7 0 - 8 0 % in mixed diet (45 - 370 mg). These results indicate that TORT- I and horse kidney are fairly homogeneous and bovine liver is slightly inhomogeneous at lower mass levels while oyster tissue and mixed diet possess some inhomogeneity with re-

spect to the distribution of Se as a function of sample weight. At the same time, it should be noted that the overall standard deviation is always less than 10% for 50 mg samples of bovine liver and oyster tissue and for 250 mg samples of mixed diet. The variability of the overall standard deviation as a function of sample weight is well demonstrated in Fig. 4.

Table 6 lists the results of a one-way analysis of variance for the data presented in Tables 1 to 5 along with the mea-

Table 6. Results of homogeneity tests for Se in biological reference materials by CINAA

405

Reference material Se concentration Analysis of variance

Pooled avg. Certified value DF, DF, +_ SD between within

samples samples (I--1) I (J--l)

F = , ( I - 1 ) , l ( J - i) p value 2 2

GB/G w

Tabulated F value

NRC lobster hepatopancreas 6.66 + 0.49 6.88_+ 0.47 4 25 IAEA horse kidney 4.88 +_ 0.23 4.67 + 0.30 4 22 NBS oyster tissue 2.22_+ 0.27 2.1 +_ 0.5 4 25 NBS mixed diet 259 ± 49" 242 _+ 30 a 3 20 NBS bovine liver (1577a) 715 ___ 56 a 710 _+ 70 a 4 25

0.13 0.97 2.76 0.58 0.68 2.82 0.29 0.88 2.76 0.21 0.89 3.10 0.84 0.51 2.76

ain ng/g, all other concentrations are in gg/g

3 0

2 0

t 0

0 I 0 2 0 3 O.

Weight (g)

Fig. 4. The variation of overall standard deviation (So, %) with subsampling weight of the reference materials. * TORT-l, A horse kidney, © oyster tissue, 49 bovine liver, [] mixed diet

r-} O.

C 0 4J

0 U

OJ CO

'H.

61 'i 3

oF

T

I I i

f I T- .I-

T

I . . . .

l .L

~n m z ~ - - - - ~ - - - G - - - - -

) , I , I , I ,

0 100 H00 300 400

W e i g h t (rag) Fig. 5. The variation of Se content as a function of sample weight of the reference materials. * TORT-l, A horse kidney, © oyster tissue, 49 bovine liver, [] mixed diet, - - poold avg., - - - certified value

sured pooled average and the certified values. The agreement between measured pooled average Se concentrat ions and certified values is good. The variabi l i ty in measured Se concentrat ion as a function of sample weight is shown in Fig. 5.

A 6 x 5 (for T O R T - l , oyster tissue and bovine liver) and 6 × 4 (for horse kidney and mixed diet) matrices were used in evaluating the heterogeneity of the subsampling opera- tion. The relative magni tude of the between-weight-range to within-weight-range sample homogenei ty is given by the F- ratio. The computed and the tabula ted F values at the 95% confidence level for 4 (or 3) between-weight-range and 25 (or 20) within-weight-range degrees of freedom are shown in Table 6. All computed F-results are below the tabula ted

F-values indicating that the between-weight-range sample homogenei ty is statistically as good as within-weight-range homogenei ty for all the reference materials investigated.

In order to compare the sampling constant value for Se in oyster tissue obtained through the short-l ived nuclide 77mSe by C I N A A with that calculated using the long-lived 7SSe, and to estimate the sampling constants of a few selected elements via long-lived nuclides, the procedure used by Fi lby et al. [13] was employed. A b o u t 1.2 g-sample of this SRM was i r radia ted for 24 h in the inner site of the D U S R facility. It was allowed to decay for 2 - 3 days. Six samples in the weight range of 9 - 1 1 mg were accurately weighed into separate vials and counted for 1 - 2 h. The 554-, 559- and

406

Table 7. Results of homogeneity tests for selected elements in NBS oyster tissue (SRM-1566) by INAA

Element Weight range Concentration (gg/g) (avg. wt) (nag) Individual values Measured Reported

mean _+ SD

Standard dev. (%) Ks KP "x

So Sm &

As 9-11 13.5, 12.3, 13.9 13.0 + 0.6 13.4-1- 1.9 (10.2) 12.4, 12.8, 13.0

Br 9-11 54.1, 50.8, 54.6 53.1 _+ 1.6 (55) (10.2) 51.8, 54,5, 52,8

Fe 30-33 217, 158, 216 197 _+ 26 195 -I- 34 (31.9) 223, 192, 175

Na 9-11 5174, 4956, 5077 5053 ± 115 5100 _+ 300 (10.2) 5094, 4874, 5140

Se 30-33 1.90, 2.50, 2.03 2.20-1- 0.21 2.1 _ 0.5 (31.9) 2.26, 2.33, 2.20

4.6 1.5 4.3 0.2 0.22

3.0 0.6 2.9 0.09 0.09

13.2 7.4 10.9 3.8 5.6

2.3 0.9 2.1 0.05 0.05

9.6 5.1 8.1 2.1 2.9

1369-keV photopeaks were used for assaying S2Br, 76As and 24Na, respectively. Another six samples in the weight range of 3 0 - 33 mg were weighed separately and counted for 1 - 2 h after a decay of 20 d. The 265- and 1099-keV peaks were used for 75Se and 59Fe, respectively. The elemental comparator standards were also run under identical conditions of irradiation, decay, counting, and sample geometry. The concentration of As, Br, Fe, Na and Se were determined and the results are shown in Table 7 along with the reported values for comparison purposes. The Se content of oyster tissue obtained by CINAA (2.22 + 0.27, Table 6) compares very well with that of INAA (2.20 + 0.21, Table 7). The values measured for other elements by INAA agree well with the reported values. The overall measurement, and subsampling standard deviations together with the sampling constant calculated are also presented in Table 7.

The homogeneity of a reference material can be enhanced by decreasing the particle size and/or increasing the amount of mixing during the preparation step. The homogeneity of certain CRM's can be related to their methods of preparation. For example, TORT-1 was prepared by acetone extrac- tion of lobster tomalle and therefore one would expect a fair homogeneity in the sample, as also observed in this work. In another situation, the homogeneity for Se in a CRM can depend on the way it is distributed within a tissue or organ. Selenium may be incorporated into a protein and homogeneously distributed or it may be concentrated at a specific area of an organ leading to more inhomogeneity in the sample. It has been observed in our laboratory over the last 4 - 5 years that Se is evenly distributed in bovine kidneys. The same could very well be the situation with horse kidney. Mixed diet reference material [36], on the other hand, was prepared by mixing many different food items representative of a U.S. daily diet. The inhomogeneous distribution of Se in this RM below about 250 mg may be due to the complexity of its constituents.

Ingamell's sampling constant (Ks)

The estimation of Ingamell's sampling constant (Ks) depends on how best the measurement uncertainty (Sin) can be differentiated from subsampling uncertainty (Ss). If Sm is at least two times smaller than So, then a reasonable number of measurements shall provide a reliable value for Ss. On the other hand, if Sm is slightly less or almost equal to So, a large

number of determinations are needed to clearly distinguish between Sm and So.

The selection of an appropriate weight range is another important parameter for estimating sampling constants. The use of fairly low-weight range samples with low measurement errors facilitate the calculation of sampling constant. How- ever, it becomes more and more difficult to keep the measurement error under good statistical control at lower sample masses mainly because of the decrease in sensitivity and increase in reagent blanks. On the other hand, the use of a larger sample mass provides good sensitivity and brings the analytical uncertainty under strict statistical control but the significance of inhomogeneity is decreased drastically. Therefore, the selection of an optimum sample mass helps to reliably calculate Ks. When a reasonably constant Ks value is obtained from subsamples which appreciably differ in size, it not only establishes the absence of segregation but also helps in more reliably calculating the minimum weight of the sample required for any preselected So value. I f the measurement and overall uncertainties do not differ much from each other, then the overall standard deviation should be used in the estimation of sampling constant which is termed as/~ax.

The value of Ss is 2-- 3 times larger than Sm for oyster tissue (Table 3) and mixed diet (Table 4) in the weight range 5 - 5 0 m g and 4 5 - 1 1 0 m g , respectively. For TORT-I (Table 1) and bovine liver (Table 5), Ss is almost one and half-times larger than Sm in the weight range 5 - 1 0 mg. These observations suggest that the suitable weight ranges for conveniently calculating Ks values are < 5 mg for horse kidney, 5 - 1 0 mg for TORT-1 and bovine liver, 5 - 5 0 mg for oyster tissue, and 45 - 110 mg for mixed diet.

A plot of subsampling variance (S 2 %) vs. the reciprocal of the mean sample weight in g (l/W) for each weight range should yield a straight line according to the equation S 2 = Ks/W. The slope of the line gives the value of Ks with the intercept being zero in principle. A weighted least squares fitting was done on the data and the calculated Ks values are presented in Table 8.

The sample constants (Ks and/Q~ax) calculated for As, Br, Fe, Na and Se in oyster tissue by INAA are shown in Table 7. A comparison of the sampling constants calculated for Se in oyster tissue by long irradiation (2.9 g, Table 7) and by CINAA (3.3 g, Table 8) reveals that /~ ,x values are almost the same. The difference in Ks values determined by long irradiation INAA (2.1 g) and by CINAA (3.0 g) could

407

Table 8. Sampling constants for Se in selected biological reference materials

Reference material Sampling constant (g)

K s /~ss ax

NRC lobster hepatopancreas 0.9 1.2 IAEA horse kidney 0.03 0.3 NBS oyster tissue 3.0 3.3 NBS mixed diet 30.9 37.5 NBS bovine liver (1577a) 0.9 1.7

be a t t r ibuted to the ease in differentiat ion of So and S m due to the less background interference from already decayed 24Na and 3aC1 in the I N A A method. However, the long irradiat ion, decay, and counting times required for assaying the long-lived 75Se do not permit the I N A A method to be used in analyzing a large number of samples necessary to determine the sampling constant . The results indicate that the K~ values for Se range from 0.04 to about 3.0 g in four of the reference materials and is about 31 g in mixed diet.

Conclusions

Selenium concentrat ions determined by C I N A A in this work for lobster hepatopancreas , horse kidney, oyster tissue, mixed diet and bovine liver agree well with the certified values. It has been shown by a one-way analysis of variance that the between-weight-range heterogeneity is no greater than within-weight-range heterogeneity for Se in all five reference materials. The subsampling uncertainties are less than the measurement uncertainties in horse kidney (all weight ranges) and TORT-1 ( > 5 rag), and slightly higher in bovine liver indicat ing that these materials are adequately homogeneous for Se. In oyster tissue and mixed diet, Ss is 2 - 3 times larger than Sm suggesting a heterogeneous dis t r ibut ion of Se. The Ks values for Se determined in this work can be used to a fair degree of confidence to calculate the min imum weight of sample required for a preselected s tandard deviation.

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Received June 22, 1990

determination of sampling constants for selenium in biological reference materials by neutron...

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